SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

doi:10.1016/S0252-9602(17)30069-3

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1221-1229.doi: 10.1016/S0252-9602(17)30069-3

SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

吐尔德别克

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

收稿日期:2016-10-25 修回日期:2016-12-12 出版日期:2017-10-25 发布日期:2017-10-25
作者简介:Turdebek N. BEKJAN,E-mail:bekjant@yahoo.com
基金资助:
The research is supported by NSFC (11371304).

SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

Turdebek N. BEKJAN

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Received:2016-10-25 Revised:2016-12-12 Online:2017-10-25 Published:2017-10-25
Supported by:
The research is supported by NSFC (11371304).

摘要/Abstract

摘要：

Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let A be a maximal subdiagonal algebra of M. We proved a Szegö type factorization theorem for the Haagerup noncommutative H^p-spaces.

关键词: subdiagonal algebras, Haagerup noncommutative H^p

Abstract:

Key words: subdiagonal algebras, Haagerup noncommutative H^p

吐尔德别克. SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES[J]. 数学物理学报(英文版), 2017, 37(5): 1221-1229.

Turdebek N. BEKJAN. SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES[J]. Acta mathematica scientia,Series B, 2017, 37(5): 1221-1229.

参考文献

[1] Adurexit A, Bekjan T N. Noncommutative Orlicz-Hardy spaces. Acta Math Sci, 2014, 34B(5):1584-1592
[2] Arveson W B. Analyticity in operator algebras. Amer J Math, 1967, 89:578-642
[3] Bekjan T N, Xu Q. Riesz and Szegö type factorizations for noncommutative Hardy spaces. J Oper Theory, 2009, 62(1):215-231
[4] Blecher D P, Labuschagne L E. Applications of the Fuglede-Kadison determinant:Szegö's theorem and outers for noncommutative H^p. Trans Amer Math Soc, 2008, 360:6131-6147
[5] Blecher D P, Labuschagne L E. A Beurling theorem for noncommutative L^p. J Operator Theory, 2008, 59:29-51
[6] Blecher D P, Labuschagne L E. Outers for noncommutative H^p revisited. Studia Math, 2013, 217:265-287
[7] Haagerup U. L^p-spaces associated wth an arbitrary von Neumann algegra. Algèbres d'opérateurs et leurs applications en physique mathématique (Proc Colloq, Marseille, 1977), Vol 274 of Colloq Internat CNRS, Paris, 1979:175-184
[8] Haagerup U. The standard form of von Neumann algebras. Math Scand, 1975, 37:271-283
[9] Ji G, Ohwada T, Saito K-S. Certain structure of subdiagonal algebras. J Operator Theory, 1998, 39:309-317
[10] Ji G, Saito K-S. Factorization in subdiagonal algebras. J Funct Anal, 1998, 159:191-202
[11] Ji G. A noncommutative version of H^p and characterizations of subdiagonal algebras. Integr Equ Oper Theory, 2012, 72:183-191
[12] Ji G. Analytic Toeplitz algebras and the Hilbert transform associated with a subdiagonal algebra. Sci China Math, 2014, 57:579-588
[13] Junge M, Xu Q. Noncommutative Burkholder/Rosental inequalities. Ann Prob, 2003, 31:948-995
[14] Labuschagne L E. Analogues of composition operators on non-commutative H^p spaces. J Operator Theory, 2003, 49:115-141
[15] Labuschagne L E. Invariant subspaces for H² space of σ-finite algebras. Bull London Math Soc, 2017, 49(1):33-44
[16] Marsalli M, West G. Noncommutative H^p-spaces. J Operator Theory, 1997, 40:339-355
[17] Marsalli M, West G. The dual of noncommutative H¹. Indiana Univ Math J, 1998, 47:489-500
[18] Pedersen G K, Takesaki M. The Radon-Nikodym theorem for von Neuman algebras. Acta Math, 1973, 130:53-87
[19] Pisier G, Xu Q. Noncommutative L^p-spaces//Handbook of the Geometry of Banach Spaces, Vol 2. Elsevier, 2003:1459-1517
[20] Randrianantoanina N. Hilbert transform associated with finite maximal subdiagonal algebras. J. Austral Math Soc (Series A), 1999, 65:388-404
[21] Saito K-S. A note on invariant subspaces for maximal subdiagonal algebras. Proc Amer Math Soc, 1979, 77:349-352
[22] Shao J, Han Y. Szego type factorization theorem for noncommutative Hardy-Lorentz space. Acta Math Sci, 2013, 33B(6):1675-1684
[23] Takesaki M. Tomita's Theory of Modular Hilbert Algebras and Applications. Lect Notes in Math, Vol 128. Berlin-New York:Springer-Verlag, 1970
[24] Terp M. L^p-spaces associated wth an arbitrary von Neumann algegras. Notes, Math Institute, Copenhagen Univ, 1981
[25] Xu Q. On the maximality of subdiagonal algebras. J Operator Theory, 2005, 54:137-146

SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

Metrics

本文评价

推荐阅读 10